I have a rx7 series 5 13 B turbo motor the car starts and runs really well but once the car warms up its starts smoking and increases then after driving it the smoke starts to die down alot

It has a seeping head gasket! This is a common problem with all import engines. They are not designed to run hot! Even if they have a lot of miles on them, this problem always seem to follow. If you are familiar with running compression test on a engine, I highly suggest you run one on your engine. Run a compression test with it cold and after the engine is warmed up. If the compression is lower once the engine is warm, your head gasket is leaking compression, and its pulling oil from between the gasket into the cylinders causing the smoke. Or it can be a combination of a seeping head gasket and a bad oil seal on the turbo too as well....

White smoke comes in two forms

On start up it can be unburnt fuel

While driving vehicle, motor warmed up ,
it is coolant in the exhaust,usually a bad head
gasket

If your bmw has a turbo,then a problem there,
from motor oil associated with turbo problem

There can be several reasons for this. You can have worn valve stem seals on the valves, which may change with warm oil, or you have worn oil rings in the cylinders.

A compression test when the engine is cold would reveal if the piston rings are worn. Another possibility could be a bad head gasket which leaks oil when cold and then seals when the heads warm. A compression test would also diagnose this.

Rings maybe?? Run it till it smokes then remove a couple of glow plugs & inspect the bores to look for evidence of oil. Does it smoke when u first start it too?? Or only once it has warmed up??

If your after market turbo is blowing oil into the engine, best you have it removed. When you say that fuel may be leaking into the cylinders, it could be leaking fuel injectors. If the smoke out of the tail pipe, it's usually indicator of burning coolant. Blue smoke is indicator of fuel and black of oil.

did you install the filter the correct way
sounds like the pump is not working properly
a faulty regulator will dump excess fuel

Certainly sounds like a head gasket. The coolant level will take a while to drop, but it will. A cup of coolant can make a lot of steam, and and oil would be blue smoke, not white.
Try running it with the rad cap off, and see if there is a constant flow of bubbles coming up in the rad. If there is, it's bad news.
Good luck.

1st you need to do a compression test.Check for blocked exhaust. smoke from turbo could indicate and internal engine oil seal issue.

YOU MAY HAVE BLOCKED OIL RETURN HOLES,REMOVE VALVE COVER AND CH# THE 2 F/R

well,when you turn off the rotary it leaves oil and gas.so when you start it up, it burns off the oil you left causeing blueish smoke. same problem with flooding,when you drive short distance , warmup incorrectly or if use synthetic oil.to fix the cause of flooding(i have the same vehicle and problems)let it warm up for at least 15 min.there is also a fuel pump wire next to the fuse box located above the brake pedal.then you tap a switch from the fuel pump to your interior.the reoson being is so whenever you come to a stop to park flip the swith.that allows the rotar to burn the fuel left in the pump witch will make your rx7 to stutter out and die.when you start it back up ,flip the swicth back on and it will take an extra second for it to crank over.1 more thing,check your oil every 2-3 fills on gas and change oil every 2000 miles.also redline it at least one a week. i hope i just solved your problem because i love my 87 non turbo and know how you feel.if you want to look at cheap aftermarket parts for rx7 then go to srmotorsports.com/rx7guru.com is a guy that test parts to tell people wats good and cheap for rx7s.i would recomend roll cage and 5 point harness-seats.good luck with your rx7 bro